EP4736302A1

EP4736302A1 - Reluctance actuator, positioning device, stage apparatus, lithographic apparatus

Info

Publication number: EP4736302A1
Application number: EP24730372.0A
Authority: EP
Inventors: Sjoerd Martijn HUIBERTS; Maarten Hartger Kimman; Johannes Marinus Maria Rovers
Original assignee: ASML Netherlands BV
Current assignee: ASML Netherlands BV
Priority date: 2023-06-29
Filing date: 2024-06-04
Publication date: 2026-05-06
Also published as: WO2025002731A1; CN121420458A; KR20260028700A; TW202519997A

Abstract

The invention provides a reluctance actuator configured to exert a substantially upward force on an object, that is displaceable by a mover of a positioning device in a horizontal direction, the reluctance actuator comprising: a first member configured to be connected to the object, a second member configured to be connected to the mover, the first and second member forming a magnetic flux path comprising a gap between the first member and the second member, a permanent magnet arranged in the magnetic flux path to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member and a coil configured to engage with either the first member or the second member and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member.

Description

RELUCTANCE ACTUATOR, POSITIONING DEVICE, STAGE APPARATUS, LITHOGRAPHIC

APPARATUS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23182537.3 which was filed on 29 June 2023 and which is incorporated herein in its entirety by reference.

FIELD

[0002] The present invention relates to reluctance actuators and positioning devices for use in a lithographic apparatus.

BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) of a patterning device (e.g., a mask) onto a layer of radiation- sensitive material (resist) provided on a substrate (e.g., a wafer).

[0004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as ‘Moore’s law’. To keep up with Moore’s law the semiconductor industry is chasing technologies that enable to create increasingly smaller features. To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within a range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[0005] In order to ensure an accurate positioning of the pattern on the substrate, it is important to ensure that the patterning device, holding the pattern, and the substrate are accurately positioned relative to each other. In order to achieve this, positioning devices are applied which often combine one or more electromagnetic motors, for displacing the patterning device or substrate over comparatively large distances, and one or more electromagnetic actuators, for displacing the patterning device or substrate over comparatively small distances, with a high accuracy.

[0006] At the same time, there is a constant need to increase the throughput of a lithographic apparatus, which typically requires an increase in power for both the electromagnetic motors and the actuators. Achieving an increase in throughput using known positioning devices is found to be difficult, in particular with respect to the applied electromagnetic motors for the comparatively large displacements. This difficulty is at least partly caused by the applied electromagnetic actuators. The currently applied actuators have mainly been optimised to achieve an accurate positioning and a high efficiency. As a result, such actuators typically operate with very small operating ranges. It has been observed that these small operating ranges pose a limit to the design freedom of the positioning device, thus limiting the options to achieve a higher throughput. There is therefore a need for a different type of actuator which enables a larger design freedom for a positioning device.

SUMMARY

[0007] It is an objective of the present invention to provide an actuator enabling a larger design freedom when the actuator is applied in a positioning device of a lithographic apparatus.

[0008] According to an aspect of the invention, there is provided a reluctance actuator configured to exert a substantially upward force on an object, that is displaceable by a mover of a positioning device in a horizontal direction, the reluctance actuator comprising: a first member configured to be connected to the object; a second member configured to be connected to the mover; the first and second member forming a magnetic flux path comprising a gap between the first member and the second member; a permanent magnet arranged in the magnetic flux path to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member; a coil configured to engage with either the first member or the second member and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member; a first surface of the first member and a first surface of the second member which face each other across the gap are configured to maintain a magnetic flux resistance of the magnetic flux path substantially constant for a displacement of the first member relative to the second member in the horizontal direction over a predetermined distance D.

[0009] According to another aspect of the present invention, there is provided a positioning device for positioning an object table, the positioning device comprising: a linear or planar motor for positioning the object table over comparatively large distances, the linear or planar motor comprising: a stator; a mover configured to displace the object table relative to the stator; wherein the positioning device further comprises one or more reluctance actuators according to the invention, whereby first members of the one or more reluctance actuators are configured to be connected to the object table, as the object, and whereby second members of the one or more reluctance actuators are connected to the mover. [00010] The positioning device according to the present invention may advantageously be applied in a stage apparatus, which stage apparatus can e.g. be applied in an exposure apparatus or a lithographic apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

[00011] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

Figure 1 depicts a schematic overview of a lithographic apparatus;

Figure 2 depicts a detailed view of a part of the lithographic apparatus of Figure 1;

Figure 3 schematically depicts a position control system;

Figure 4 depicts a first embodiment of a reluctance actuator according to the present invention;

Figure 5 depicts an YZ-view of the reluctance actuator of Figure 4;

Figure 6 depicts an XZ-view of the reluctance actuator of Figure 4;

Figure 7 depicts a second embodiment of a reluctance actuator according to the present invention;

Figure 8 depicts a third embodiment of a reluctance actuator according to the present invention.

Figures 9 (a) and 9 (b) depict a fourth and fifth embodiment of a reluctance actuator according to the present invention.

Figure 10 depicts a sixth embodiment of a reluctance actuator according to the present invention.

Figure 11 depicts a seventh embodiment of a reluctance actuator according to the present invention.

DETAILED DESCRIPTION

[00012] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[00013] The term “reticle”, “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective, binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array.

[00014] Figure 1 schematically depicts a lithographic apparatus LA. The lithographic apparatus LA includes an illumination system (also referred to as illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation or EUV radiation), a mask support (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA in accordance with certain parameters, a substrate support (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support in accordance with certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[00015] In operation, the illumination system IL receives a radiation beam from a radiation source SO, e.g. via a beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and/or other types of optical components, or any combination thereof, for directing, shaping, and/or controlling radiation. The illuminator IL may be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in its cross section at a plane of the patterning device MA.

[00016] The term “projection system” PS used herein should be broadly interpreted as encompassing various types of projection system, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and/or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, and/or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system” PS.

[00017] The lithographic apparatus LA may be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system PS and the substrate W - which is also referred to as immersion lithography. More information on immersion techniques is given in US6952253, which is incorporated herein by reference.

[00018] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also named “dual stage”). In such “multiple stage” machine, the substrate supports WT may be used in parallel, and/or steps in preparation of a subsequent exposure of the substrate W may be carried out on the substrate W located on one of the substrate support WT while another substrate W on the other substrate support WT is being used for exposing a pattern on the other substrate W.

[00019] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measurement stage. The measurement stage is arranged to hold a sensor and/or a cleaning device. The sensor may be arranged to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning device may be arranged to clean part of the lithographic apparatus, for example a part of the projection system PS or a part of a system that provides the immersion liquid. The measurement stage may move beneath the projection system PS when the substrate support WT is away from the projection system PS. [00020] In operation, the radiation beam B is incident on the patterning device, e.g. mask, MA which is held on the mask support MT, and is patterned by the pattern (design layout) present on patterning device MA. Having traversed the patterning device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position measurement system IF, the substrate support WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor (which is not explicitly depicted in Figure 1) may be used to accurately position the patterning device MA with respect to the path of the radiation beam B. Patterning device MA and substrate W may be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks Pl, P2 as illustrated occupy dedicated target portions, they may be located in spaces between target portions. Substrate alignment marks Pl, P2 are known as scribe-lane alignment marks when these are located between the target portions C.

[00021] To clarify the invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axis, i.e., an x-axis, a y-axis and a z-axis. Each of the three axis is orthogonal to the other two axis. A rotation around the x-axis is referred to as an Rx-rotation. A rotation around the y- axis is referred to as an Ry-rotation. A rotation around about the z-axis is referred to as an Rz-rotation. The x-axis and the y-axis define a horizontal plane, whereas the z-axis is in a vertical direction. The Cartesian coordinate system is not limiting the invention and is used for clarification only. Instead, another coordinate system, such as a cylindrical coordinate system, may be used to clarify the invention. The orientation of the Cartesian coordinate system may be different, for example, such that the z-axis has a component along the horizontal plane.

[00022] Figure 2 shows a more detailed view of a part of the lithographic apparatus LA of Figure 1. The lithographic apparatus LA may be provided with a base frame BF, a balance mass BM, a metrology frame MF and a vibration isolation system IS. The metrology frame MF supports the projection system PS. Additionally, the metrology frame MF may support a part of the position measurement system PMS. The metrology frame MF is supported by the base frame BF via the vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce vibrations from propagating from the base frame BF to the metrology frame MF.

[00023] The second positioner PW is arranged to accelerate the substrate support WT by providing a driving force between the substrate support WT and the balance mass BM. The driving force accelerates the substrate support WT in a desired direction. Due to the conservation of momentum, the driving force is also applied to the balance mass BM with equal magnitude, but at a direction opposite to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the masses of the moving part of the second positioner PW and the substrate support WT.

[00024] In an embodiment, the second positioner PW is supported by the balance mass BM. For example, wherein the second positioner PW comprises a planar motor to levitate the substrate support WT above the balance mass BM. In another embodiment, the second positioner PW is supported by the base frame BF. For example, wherein the second positioner PW comprises a linear motor and wherein the second positioner PW comprises a bearing, like a gas bearing, to levitate the substrate support WT above the base frame BF.

[00025] The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the substrate support WT. The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the mask support MT. The sensor may be an optical sensor such as an interferometer or an encoder. The position measurement system PMS may comprise a combined system of an interferometer and an encoder. The sensor may be another type of sensor, such as a magnetic sensor, a capacitive sensor or an inductive sensor. The position measurement system PMS may determine the position relative to a reference, for example the metrology frame MF or the projection system PS. The position measurement system PMS may determine the position of the substrate table WT and/or the mask support MT by measuring the position or by measuring a time derivative of the position, such as velocity or acceleration.

[00026] The position measurement system PMS may comprise an encoder system. An encoder system is known from for example, United States patent application US2007/0058173A1, filed on September 7, 2006, hereby incorporated by reference. The encoder system comprises an encoder head, a grating and a sensor. The encoder system may receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam as well as the secondary radiation beam originate from the same radiation beam, i.e., the original radiation beam. At least one of the primary radiation beam and the secondary radiation beam is created by diffracting the original radiation beam with the grating. If both the primary radiation beam and the secondary radiation beam are created by diffracting the original radiation beam with the grating, the primary radiation beam needs to have a different diffraction order than the secondary radiation beam. Different diffraction orders are, for example, + 1^st order, -1^st order, +2^nd order and -2^nd order. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. A sensor in the encoder head determines a phase or phase difference of the combined radiation beam. The sensor generates a signal based on the phase or phase difference. The signal is representative of a position of the encoder head relative to the grating. One of the encoder head and the grating may be arranged on the substrate structure WT. The other of the encoder head and the grating may be arranged on the metrology frame MF or the base frame BF. For example, a plurality of encoder heads are arranged on the metrology frame MF, whereas a grating is arranged on a top surface of the substrate support WT. In another example, a grating is arranged on a bottom surface of the substrate support WT, and an encoder head is arranged below the substrate support WT.

[00027] The position measurement system PMS may comprise an interferometer system. An interferometer system is known from, for example, United States patent US6,020,964, filed on July 13, 1998, hereby incorporated by reference. The interferometer system may comprise a beam splitter, a mirror, a reference mirror and a sensor. A beam of radiation is split by the beam splitter into a reference beam and a measurement beam. The measurement beam propagates to the mirror and is reflected by the mirror back to the beam splitter. The reference beam propagates to the reference mirror and is reflected by the reference mirror back to the beam splitter. At the beam splitter, the measurement beam and the reference beam are combined into a combined radiation beam. The combined radiation beam is incident on the sensor. The sensor determines a phase or a frequency of the combined radiation beam. The sensor generates a signal based on the phase or the frequency. The signal is representative of a displacement of the mirror. In an embodiment, the mirror is connected to the substrate support WT. The reference mirror may be connected to the metrology frame MF. In an embodiment, the measurement beam and the reference beam are combined into a combined radiation beam by an additional optical component instead of the beam splitter.

[00028] The first positioner PM may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT relative to the long-stroke module with a high accuracy over a small range of movement. The short-stroke module may e.g. comprise a set of actuators to position the mask support MT in multiple degrees of freedom, e.g. 6 degrees of freedom. In an embodiment, the present invention provides a positioning device which can serve as the first positioner PM and which comprises a set of reluctance actuators according to the invention for positioning the mask support MT. The set of reluctance actuators may e.g. be applied to position the mask support MT in the vertical direction. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. In order to do so, the long-stroke module may e.g. have a mover that is supporting or holding the short-stroke module and a stator co-operating with the mover to displace the mover over the large range of movement. The large range of movement e.g. being oriented in a substantially horizontal direction. Note that in such an arrangement, the stator need not to remain stationary during operation, the stator may also be mounted on a balance mass. With the combination of the long-stroke module and the short-stroke module, the first positioner PM is able to move the mask support MT relative to the projection system PS with a high accuracy over a large range of movement.

[00029] Similarly, the second positioner PW may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT relative to the long- stroke module with a high accuracy over a small range of movement. The short-stroke module may e.g. comprise a set of actuators to position the substrate support WT in multiple degrees of freedom, e.g. 6 degrees of freedom. In an embodiment, the present invention provides a positioning device which can serve as the second positioner PW and which comprises a set of reluctance actuators according to the invention for positioning the substrate support WT. The set of reluctance actuators may e.g. be applied to position the substrate support WT in the vertical direction. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. In order to do so, the long-stroke module may e.g. have a mover that is supporting or holding the short-stroke module and a stator co-operating with the mover to displace the mover over the large range of movement. The large range of movement e.g. being oriented in a substantially horizontal plane. Note that in such an arrangement, the stator need not to remain stationary during operation, the stator may also be mounted on a balance mass. With the combination of the long- stroke module and the short- stroke module, the second positioner PW is able to move the substrate support WT relative to the projection system PS with a high accuracy over a large range of movement. [00030] The first positioner PM and the second positioner PW each are provided with an actuator to move respectively the mask support MT and the substrate support WT. The actuator may be a linear actuator to provide a driving force along a single axis, for example the y-axis. Multiple linear actuators may be applied to provide driving forces along multiple axis. The actuator may be a planar actuator to provide a driving force along multiple axis. For example, the planar actuator may be arranged to move the substrate support WT in 6 degrees of freedom. The actuator may be an electro-magnetic actuator comprising at least one coil and at least one magnet. The actuator is arranged to move the at least one coil relative to the at least one magnet by applying an electrical current to the at least one coil. The actuator may be a moving-magnet type actuator, which has the at least one magnet coupled to the substrate support WT respectively to the mask support MT. The actuator may be a moving-coil type actuator which has the at least one coil coupled to the substrate support WT respectively to the mask support MT. The actuator may be a voice-coil actuator, a reluctance actuator, a Lorentz-actuator or a piezo-actuator, or any other suitable actuator.

[00031] The lithographic apparatus LA comprises a position control system PCS as schematically depicted in Figure 3. The position control system PCS comprises a setpoint generator SP, a feedforward controller FF and a feedback controller FB. The position control system PCS provides a drive signal to the actuator ACT. The actuator ACT may be the actuator of the first positioner PM or the second positioner PW. The actuator ACT drives the plant P, which may comprise the substrate support WT or the mask support MT. An output of the plant P is a position quantity such as position or velocity or acceleration. The position quantity is measured with the position measurement system PMS. The position measurement system PMS generates a signal, which is a position signal representative of the position quantity of the plant P. The setpoint generator SP generates a signal, which is a reference signal representative of a desired position quantity of the plant P. For example, the reference signal represents a desired trajectory of the substrate support WT. A difference between the reference signal and the position signal forms an input for the feedback controller FB. Based on the input, the feedback controller FB provides at least part of the drive signal for the actuator ACT. The reference signal may form an input for the feedforward controller FF. Based on the input, the feedforward controller FF provides at least part of the drive signal for the actuator ACT. The feedforward FF may make use of information about dynamical characteristics of the plant P, such as mass, stiffness, resonance modes and eigenfrequencies. [00032] Figure 4 schematically shows a reluctance actuator 400 according to the present invention. Such an actuator may e.g. be applied in the aforementioned first positioner or second positioner, in particular as part of the mentioned short-stroke modules. In particular, the reluctance actuator according to the invention may be applied to support an object, e.g. an object table such as the mask support MT or the substrate support WT, and to control a position of said object in the vertical direction. The actuator 400 as shown comprises a first member 410 and a second member 420. The first member and the second member of the reluctance actuator according to the invention may also be referred to as magnetic member, i.e. members made from or comprising a magnetically conductive material. The first member 410 is configured to be connected to the object that is supported. In the embodiment as shown, the first member 410 comprises a C-core structure 412 and a connection member 414 for connecting to the object that is supported. In the embodiment as shown, the connection member 414 has a bottom end 414.1 connected to the C-core structure 412 of the first member 410 and a top end 414.2 configured to be connected to the object. In the embodiment as shown, the top end 414.2 is, during use, arranged above a top surface 420.1 of the second member 420.

[00033] In accordance with the invention, the second member 420 is configured to be connected to a mover of a positioning device for displacing the object in the horizontal direction. Such a positioning device can e.g. be the aforementioned first positioner PM or the second positioner PW.

[00034] In accordance with the invention, the first member 410 and the second member 420 form a magnetic flux path, indicated by the dotted line 440 which comprises a gap 450 between the first member 410 and the second member 420. The reluctance actuator 400 according to the present invention further comprises a permanent magnet 460 that is arranged in the magnetic flux path 440 and which is configured to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member 410. In the embodiment as shown, the permanent magnet or magnets 460 are arranged in the magnetic flux path of the second member 420. Note that, in an alternative embodiment, the permanent magnet or magnets may also be arranged in the magnetic flux path of the first member 410. In an embodiment, the bias upward force of the actuator can be configured to counteract a substantial part of the weight of the object.

[00035] The reluctance actuator 400 further comprises a coil 470 configured to engage with either the first member 410 or the second member 420 and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member 410. In the embodiment as shown, the coil 470 is wound about a part of the second member 420. The variable force as generated can e.g. be applied for accurate positioning of the object to which the first member 410 is connected, during use.

[00036] In accordance with the present invention, a first surface of the first member 410 and a first surface of the second member 420 which face each other across the gap 450 are configured to maintain a magnetic flux resistance of the magnetic flux path 440 substantially constant for a displacement of the first member relative to the second member in a horizontal direction, e.g. in the indicated X-direction or Y -direction over a predetermined distance. This is illustrated in more detail below. In order to ensure that the magnetic flux resistance remains substantially constant for a displacement in the horizontal direction across the predetermined distance, one can select the facing first surfaces to have different sizes.

[00037] The reluctance actuator according to the present invention provides, due to the design characteristics mentioned above, an additional operational freedom for the positioning device that moves the object in the horizontal direction. This can be understood as follows. When the reluctance actuator, e.g. actuator 400, is applied for accurate positioning of an object, e.g. as part of a short-stroke module as mentioned above, the object is typically controlled to follow a particular trajectory, e.g. a trajectory in an XY-plane during which the object can undergo different processes. In known positioning devices, the mover of the positioning device, e.g. part of a long-stroke module as mentioned above, is required to substantially follow the same trajectory in the XY-plane. This is due to the fact that known vertical actuators as e.g. applied in short-stroke modules are not designed to allow displacements in the horizontal plane. However, using the reluctance actuator according to the invention enables or allows a horizontal displacement of the mover of the positioning device relative to the object. This is due to the particular design of the reluctance actuator according to the invention, whereby the mover is connected to the second member of the reluctance actuator, the object is connected to the first member of the reluctance actuator and the actuator is designed to allow a displacement in the horizontal direction over a predetermined distance. This offers an additional operational freedom for the positioning device in that the mover of the positioning device need not exactly follow the object. This additional operational freedom can e.g. allow the mover to lag behind the object instead of following the object. As such, less power is required to operate the positioning device. In this respect, reference can e.g. be made to US 2004/0257548, incorporated herein by reference in its entirety.

[00038] Figure 5 schematically shows two views of the actuator of Figure 4 in the YZ-plane, for two different relative positions of the first and second member.

[00039] Figure 5 (a) schematically shows the first member 410 and the second member 420 of the reluctance actuator 400 of Figure 4 whereby the first member 410 is in a right most position. Note that the connection member of the first member has been omitted in Figure 5.

[00040] Figure 5 (b) schematically shows the first member 410 and the second member 420 of the reluctance actuator 400 of Figure 4 whereby the first member 410 is in a left most position.

[00041] In the embodiment as shown, the surfaces of the first and second member that face each other across the gap 450 are selected such that the magnetic flux resistance substantially remains the same, irrespective of the relative position of the first member and the second member. In the embodiment as shown, the first member 410 has a first surface 410.1 which faces a first surface 420.1 of the second member. The surface 410.1 of the first member 410 has a width W1 which is smaller than a width W2 of the surface 420.1 of the second member 420 in the Y-direction. [00042] In figure 5 (a), the surfaces 410.1 and 420.1 are aligned on the right side, in Figure 5 (b), they are aligned on the left side. As will be appreciated by the skilled person, the magnetic flux resistance will substantially be the same in both positions, as well as any position in between the positions of Figure 5 (a) and Figure 5 (b). As such, in the embodiment shown in Figures 5 (a) and (b), the first member 410 and the second member 420 can be displaces relative to each other over a distance D without a substantial variation in the generated vertical force, whereby D meets the requirement:

W2 - W1 = D (1)

[00043] As will be appreciated by the skilled person, the requirement according to equation (1) is merely a rule of thumb to obtain a magnetic flux resistance which remains substantially constant for a displacement over a distance D. For example, W2-W1 may also be larger than D, such that a magnetic flux resistance remains substantially constant for a displacement over the distance D. The actual distance or displacement which can be made, for a given expected force variation limit, will depend on various parameters such as the actual dimensions of the surfaces 410.1 and 420.1, the size of the gap 450, the level of saturation, etc... By means of simulations, e.g. Finite Element simulations, one can e.g. determine, for a given design of the first member 410 and the second member 420, the distance, also referred to as the predetermined distance D, which is allowed for the horizontal displacement of the first member 410 relative to the second member 420. As mentioned, due to possibility of displacing the first member 410 relative to the second member 420, an additional operational freedom is obtained for the positioning device, in particular a long-stroke module of such a positioning device. Referring to Figure 5, it can be understood that a position of an object that is to be displaced, and which is connected to the first member 410, can be different from a position of the mover of a positioning device, which is configured to be connected to the second member 420, in the X-direction by a distance D or smaller. Phrased differently, the mover of the positioning device need not exactly follow the set point of the object in the X-direction, due to design characteristics of the first surfaces of the first member and the second member in the X-direction. This operational freedom e.g. allows to operate the positioning device with lower power requirements.

[00044] With respect to maintaining the magnetic flux resistance substantially constant for a predetermined displacement in the indicated Y-direction, it can be pointed out that a similar effect can be obtained by designing the surface 410.1 of the first member 410 to have a width W1 that is larger than a width W2 of the surface 410.2 of the second member 420 in the Y-direction. In such case, the first member 410 and the second member 420 can be displaced relative to each other over a distance D without a substantial variation in the generated vertical force, whereby D meets the requirement:

W1 - W2 = D (2) [00045] As will be appreciated by the skilled person, the requirement according to equation (2) is merely a rule of thumb to obtain a magnetic flux resistance which remains substantially constant for a displacement over a distance D. For example, W1-W2 may also be larger than D, such that a magnetic flux resistance remains substantially constant for a displacement over the distance D.

[00046] Figure 5 schematically illustrates a possible relative displacement of the first member 410 and the second member 420 in the Y-direction. A similar displacement, i.e. a displacement which substantially does not affect the magnetic flux resistance and thus the generated vertical force, may also be possible in the X-direction. This is illustrated in Figure 6, for the reluctance actuator shown in Figure 4.

[00047] Figure 6 schematically shows two views of the actuator of Figure 4 in the XZ-plane, for two different relative positions of the first and second member.

[00048] Figure 6 (a) schematically shows the first member 410 and the second member of the reluctance actuator 400 of Figure 4 whereby the first member 410 is in a first position.

[00049] Figure 6 (b) schematically shows the first member 410 and the second member of the reluctance actuator 400 of Figure 4 whereby the first member 410 is in a second position, further to the right compared to the position in Figure 6 (a). Also for displacements along the X-direction, similar observations can be made as for displacements along the Y-direction; a width W3 of the first surface 410.1 of the first member 410 in the X-direction and a width W4 of the first surface 420.1 of the second member 420 in the X-direction can be constructed in such manner that a displacement of the first member 410 relative to the second member 420 in the X-direction does not, or hardly affects the magnetic flux resistance and thus the generated upward force.

[00050] As a result, a similar additional operational freedom as discussed with reference to Figure 5 is also obtained in the X-direction.

[00051] In the embodiment of the reluctance actuator according to the invention as illustrated in Figures 4 -6, the actuator 400 comprises a first member 410 comprising a C-core structure 412 arranged in a substantially vertical plane, and a second member 420 comprising a C-core arranged in a substantially horizontal plane.

[00052] Figure 7 schematically illustrates an alternative embodiment of a reluctance actuator according to the present invention. Figure 7 schematically shows a YZ-view of an embodiment of a reluctance actuator 700 according to the present invention which can also be applied in the aforementioned first positioner or second positioner, in particular as part of the mentioned short-stroke modules. In particular, the reluctance actuator according to the invention may be applied to support an object, e.g. an object table such as the mask support MT or the substrate support WT, and to control a position of said object in the vertical direction. The actuator 700 as shown comprises a first member 710 and a second member 720. The first member 710 is configured to be connected to the object that is supported, the object being indicated by the dotted line 702. In the embodiment as shown, the first member 710 comprises a C-core structure 712 and a connection member 714 for connecting to the object 702 that is supported.

[00053] In accordance with the invention, the second member 720 is configured to be connected to a mover of a positioning device for displacing the object in the horizontal direction. Such a positioning device can e.g. be the aforementioned first positioner PM or the second positioner PW.

[00054] In accordance with the invention, the first member 710 and the second member 720 form a magnetic flux path, indicated by the dotted line 740 which comprises a gap 750 between the first member 710 and the second member 720. The reluctance actuator 700 further comprises a permanent magnet 760 that is arranged in the magnetic flux path 740 and which is configured to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member 710. In the embodiment as shown, the permanent magnet or magnets 760 are arranged in the magnetic flux path of the second member 720. Note that, in an alternative embodiment, the permanent magnet or magnets may also be arranged in the magnetic flux path of the first member 710. In an embodiment, the bias upward force of the actuator can be configured to counteract a substantial part of the weight of the object 702.

[00055] The reluctance actuator 700 further comprises a coil 770 configured to engage with either the first member 710 or the second member 720 and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member 710. In the embodiment as shown, the coil 770 is wound about part of the second member 720. The variable force as generated can e.g. be applied for accurate positioning of the object to which the first member 710 is connected, during use.

[00056] In accordance with the present invention, a first surface 710.1 of the first member 710 and a first surface 720.1 of the second member 720 which face each other across the gap 750 are configured to maintain a magnetic flux resistance of the magnetic flux path 740 substantially constant for a displacement of the first member 710 relative to the second member 720 in a horizontal direction, i.e. the Y-direction in Figure 7, over a predetermined distance. In a similar manner as discussed with reference to Figure 5, this is realized by selecting a width W1 of the first surface 710.1 of the first member 710 smaller than a width W2 of the first surface 720.1 of the second member 720. By doing so, the aforementioned additional operational freedom for the mover of the positioning device is obtained. Compared to the reluctance actuator 400 shown in Figures 4 - 6, the reluctance actuator 700 has a first member 710 which comprises a C-core structure 712 arranged in a substantially vertical plane, and a second member 720 which comprises a C-core that is also arranged in the same substantially vertical plane, whereby the C-core of the second member 720 substantially enclosing the C-core structure 712 of the first member 710.

[00057] It can be pointed out that the first and/or second member of the reluctance actuator according to the invention may also comprises other structures apart from C-core structures. Such structures e.g. including E-core or I-core structures or structures with a circular symmetry, as illustrated below. [00058] In order to obtain a similar additional operational freedom in the X-direction, perpendicular to the YZ-plane shown in Figure 7, a width of the first surface 710.1 of the first member 710 in the X- direction can be selected smaller or larger than a width of the first surface 720.1 of the second member 720 in the X-direction.

[00059] Figure 8 schematically shows yet another example of a reluctance actuator according to the present invention.

[00060] Figure 8 schematically shows a reluctance actuator 800 which has a circular symmetry. The reluctance actuator 800 comprises a first member 810 having a top plate 812 and a bottom plate 814, the top plate 812 and the bottom plate 814 being substantially parallel to each other and spaced apart by a holder 816. The first member is configured to be connected to an object, indicated by the dotted line 802. The second member 820 of the reluctance actuator 800 is arranged in between the top plate 812 and the bottom plate 814. The second member 820 comprises an inner cylinder 822, a radially magnetized permanent magnet 824 arranged concentrically about the inner cylinder 822, a cylindrical coil 826 arranged about the inner magnetic cylinder 822, and an outer cylinder 828 arranged concentrically about the radially magnetized permanent magnet 824. In the embodiment as shown, two cylindrical coils 826 are applied, one above the permanent magnet 824 and one below the permanent magnet 824. In an embodiment, a single coil 826 may be applied as well. In the embodiment as shown, top surfaces of the inner cylinder 822 and the outer cylinder 828 are spaced apart from a bottom surface 812.1 of the top plate 812 over a distance DI, forming a first gap between the first member 810 and the second member 820. Bottom surfaces of the inner cylinder 822 and the outer cylinder 828 are spaced apart from a top surface 814.1 of the bottom plate 814 over a distance D2, forming a second gap.

[00061] The mentioned components of the first member 810, the second member 820 and the first and second gap form a magnetic flux path. In Figure 8, the dotted lines 840 illustrate the magnetic flux path of a bias magnetic flux caused by the permanent magnet 824. This bias magnetic flux will cause a vertically oriented force between the first member 810 and the second member 820. In case the second gap D2 is smaller than the first gap DI, as illustrated, the resultant force acting on the first member 810 will be an upward force. In such situation, the bias magnetic flux caused by the permanent magnet 824 thus causes an upward bias force on the first member 810. When the coils 826 are energized, i.e. supplied with a current, this can cause a variable magnetic flux in the magnetic flux path. In Figure 8, the dotted line 842 illustrates a magnetic flux path of a variable magnetic flux caused by the coils 826. Depending on the orientation of the current as applied to the coils 826, the variable magnetic flux will cause an increase or decrease of the magnetic flux crossing the first and second gap, and thus an increase or decrease of the generated upward force acting on the first member 810. As such, the current applied to the coils 826 can generate a variable force on the first member 810 and thus, during use, on the object 802.

[00062] In accordance with the present invention, the reluctance actuator 800 is configured in such manner that the first member 810 can displace relative to the second member 820 in a horizontal direction while substantially maintaining the magnetic flux resistance of the magnetic flux path. In the embodiment as shown in Figure 8, this is achieved by selecting a diameter D3 of the top plate and the bottom plate to be larger than an outer diameter D4 of the outer cylinder 828. Compared to the embodiments of Figure 4 - 7, the top and bottom surfaces of the inner and outer cylinder 822 and 828 can be considered the first surface of the first member 810, whereas the bottom surface 812.1 of the top plate 812 and the top surface 814.1 of the bottom plate 814 can be considered the first surface of the second member 820. These surfaces face each other across the gaps with distances DI and D2 and are configured to maintain a magnetic flux resistance of the magnetic flux path substantially constant for a displacement of the first member relative to the second member in the horizontal direction over a predetermined distance.

[00063] In an embodiment, the reluctance actuator according to the present invention, e.g. the actuator 400, 700 or 800, can comprise one or more sensors, such as a Hall sensor, arranged to measure a magnetic flux in the magnetic flux path. These one or more sensors or magnetic sensors can e.g. be applied at or near the surfaces of the first and/or second member of the actuator which face each other across the gap of the actuator. Based on signals obtained from these one or more sensors, a more accurate control of the generated force and or position of the actuator can be obtained.

[00064] Referring to Figure 8, such sensors can e.g. be arranged at or near the top and bottom surfaces of the inner and outer cylinders 822 and 828.

[00065] Referring to Figures 5 and 7, such sensors can e.g. be arranged at or near the surfaces 410.1 or 710.1 of the first member of the actuators 400 or 700.

[00066] Referring to Figure 8, such sensors can e.g. be arranged at or near the top and bottom surfaces of the inner and outer cylinders 822 and 828. In an embodiment of the present invention, the surfaces of the inner and/or outer cylinders 822 and 828 at which the sensors are positioned can be provided with teeth. Such teeth will cause a concentration of the magnetic flux crossing the gap at the location of said teeth. By arranging the sensors on said teeth, an improved signal-to-noise ratio can be obtained for the sensor signals. It can be pointed out that such teethed structures may also be applied to the surfaces 410.1 and 420.1 of the first and second members 410 and 420 of the actuator 400 shown in Figures 4 - 6.

[00067] Figure 9 schematically shows yet another embodiment of a reluctance actuator 900 according to the present invention.

[00068] Figure 9 schematically shows a reluctance actuator 900 which has, similar to the actuator 800 according to the invention, a circular symmetry. The reluctance actuator 900 comprises a first member 910 having a circular plate 912 and a first connection member 914, which can e.g. serve to connect to an object that is to be positioned. The circular plate 912 can e.g. be made from a magnetically conductive material. The reluctance actuator 900 further comprises a second member 920. The second member 920 comprises a magnetic member 922, a permanent magnet 924 and a coil 926. In the embodiment as shown, a gap 950 is formed between the first member 910 and the second member 920. The actuator 900 further comprises a second connecting member 928 which can e.g. serve to connect the second member 920 to a mover of a positioning device for displacing the object in the horizontal direction.

[00069] The circular plate 912 of the first member 910, the magnetic member 922, the permanent magnet 924 and the gap 950 form a magnetic flux path, as indicated by the dotted line 940. In Figure 9, the dotted line 940 illustrates the magnetic flux path of a bias magnetic flux caused by the permanent magnet 924. Such a bias magnetic flux can cause a bias upward force on the first member 910. In the embodiment as shown, the permanent magnet 924 is arranged in the magnetic flux path of the second member 920. Note that, in an alternative embodiment, the permanent magnet may also be arranged in the magnetic flux path of the first member 910, in particular in the plate 912. In an embodiment, the bias upward force of the actuator can be configured to counteract a substantial part of the weight of the object.

[00070] The reluctance actuator 900 further comprises a coil 926 configured to engage with either the first member 910 or the second member 920 and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member 910. In the embodiment as shown, the coil 926 is wound about a part of the magnetic member 922 of the second member 920. The variable force as generated can e.g. be applied for accurate positioning of the object to which the first member 910 is connected, during use.

[00071] In accordance with the present invention, surfaces of the first member 910 and the second member 920 which face each other across the gap 950 are configured to maintain a magnetic flux resistance of the magnetic flux path 940 substantially constant for a displacement of the first member relative to the second member in a horizontal direction. In particular, as will be understood by the skilled person, a displacement of the first member 910 relative to the second member 920 in radial direction, indicated by the arrow 960, will not, or hardly, affect the magnetic flux resistance along the flux path 940.

[00072] As a result, the reluctance actuator 900 according to the present invention provides, due to the design characteristics mentioned above, an additional operational freedom for the positioning device that moves the object in the horizontal direction.

[00073] With respect to the application of the one or more permanent magnets to generate a bias magnetic flux along a magnetic flux path of the reluctance actuator according to the invention, it can be mentioned that these can be positioned in either the first member and/or the second member, it can also be pointed out that the one or more permanent magnets may be applied at various locations in the first member and/or the second member, substantially without affecting the operation of the actuator. Merely as an illustration, Figure 9 (b) schematically shows a variant 900’ of the actuator 900 shown in Figure 9 (a). The reluctance actuator 900’ as schematically shown in Figure 9 (b) is identical to the actuator 900 shown in Figure 9 (a), apart from the following: compared to the actuator 900, the permanent magnet 924 of actuator 900, which can e.g. be an axially magnetized ring-shaped magnet, has been replaced by a magnet 924’, which can e.g. be a radially magnetized ring-shaped magnet. The magnet 924’ has been relocated, compared to the location of the magnet 924 of Figure 9 (a). In particular, the magnetic member 922 of the reluctance actuator 900 has been replaced by a magnetic member 922’ which comprises a pair of concentric cylinders, the permanent magnet 924’ being located in a radial gap between both cylinders. Apart from these modifications, the operation and characteristics of the actuator 900’ essentially correspond to those of the actuator 900 shown in Figure 9 (a).

[00074] Figure 10 schematically shows yet another embodiment of a reluctance actuator 1000 according to the present invention.

[00075] Figure 10 schematically shows a reluctance actuator 1000 which has, similar to the actuator 900 according to the invention, a circular symmetry. The reluctance actuator 1000 comprises a first member 1010 which can e.g. serve to connect to an object that is to be positioned. The first member 1010 can e.g. be made from a magnetically conductive material. The reluctance actuator 1000 further comprises a second member 1020. The second member 1020 comprises a magnetic member 1022, a permanent magnet 1024 and a coil 1026. In the embodiment as shown, a gap 1050 is formed between the first member 1010 and the second member 1020. The second member 1020 can e.g. serve to connect to a mover of a positioning device for displacing the object in the horizontal direction. The first member 1010 may form a circular plate or a shape suitable to form the gap 1050.

[00076] The first member 1010, the magnetic member 1022, the permanent magnet 1024 and the gap 1050 form a magnetic flux path, as indicated by the dotted line 1040. In Figure 10, the dotted line 1040 illustrates the magnetic flux path of a bias magnetic flux caused by the permanent magnet 1024. Such a bias magnetic flux can cause a bias upward force on the first member 1010. In the embodiment as shown, the permanent magnet 1024 is arranged in the magnetic flux path of the second member 1020. Note that, in an alternative embodiment, the permanent magnet may also be arranged in the magnetic flux path of the first member 1010. In an embodiment, the bias upward force of the actuator can be configured to counteract a substantial part of the weight of the object.

[00077] The reluctance actuator 1000 further comprises a coil 1026 configured to engage with either the first member 1010 or the second member 1020 and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member 1010. In the embodiment as shown, the coil 1026 is wound about a part of the magnetic member 1022 of the second member 1020. The variable force as generated can e.g. be applied for accurate positioning of the object to which the first member 1010 is connected, during use.

[00078] In accordance with the present invention, surfaces of the first member 1010 and the second member 1020 which face each other across the gap 1050 are configured to maintain a magnetic flux resistance of the magnetic flux path 1040 substantially constant for a displacement of the first member relative to the second member in a horizontal direction. In particular, as will be understood by the skilled person, a displacement of the first member 1010 relative to the second member 1020 over a distance D in radial direction, indicated by the arrow 1060, will not, or hardly, affect the magnetic flux resistance along the flux path 1040. [00079] As a result, the reluctance actuator 1000 according to the present invention provides, due to the design characteristics mentioned above, an additional operational freedom for the positioning device that moves the object in the horizontal direction.

[00080] Figure 11 schematically shows yet another embodiment of a reluctance actuator 1100 according to the present invention.

[00081] Figure 11 schematically shows a reluctance actuator 1100 which has, similar to the actuator 1000 according to the invention, a circular symmetry. The reluctance actuator 1100 comprises a first member 1110 which can e.g. serve to connect to an object that is to be positioned. The first member 1110 can e.g. be made from a magnetically conductive material. The reluctance actuator 1100 further comprises a second member 1120. The second member 1120 comprises a magnetic member 1122, a permanent magnet 1124 and a coil 1126. In the embodiment as shown, a gap 1150 is formed between the first member 1110 and the second member 1120. The second member 1120 can e.g. serve to connect to a mover of a positioning device for displacing the object in the horizontal direction. The first member 1110 is configured to have structures, for example 1111.1 and 1111.2, facing the second member 1120, thereby forming gaps 1150.1 and 1150.2.

[00082] The first member 1110, the magnetic member 1122, the permanent magnet 1124 and the gaps 1150.1, 1150.2 form a magnetic flux path, as indicated by the dotted line 1140. In Figure 11, the dotted line 1140 illustrates the magnetic flux path of a bias magnetic flux caused by the permanent magnet 1124. Such a bias magnetic flux can cause a bias upward force on the first member 1110. In the embodiment as shown, the permanent magnet 1124 is arranged in the magnetic flux path of the second member 1120. Note that, in an alternative embodiment, the permanent magnet may also be arranged in the magnetic flux path of the first member 1110. In an embodiment, the bias upward force of the actuator can be configured to counteract a substantial part of the weight of the object.

[00083] The reluctance actuator 1100 further comprises a coil 1126 configured to engage with either the first member 1110 or the second member 1120 and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member 1110. In the embodiment as shown, the coil 1126 is wound about a part of the magnetic member 1122 of the second member 1120. The variable force as generated can e.g. be applied for accurate positioning of the object to which the first member 1110 is connected, during use.

[00084] In accordance with the present invention, surfaces of the first member 1110 and the second member 1120 which face each other across the gaps 1150.1 and 1150.2 are configured to maintain a magnetic flux resistance of the magnetic flux path 1140 substantially constant for a displacement of the first member relative to the second member in a horizontal direction. In particular, as will be understood by the skilled person, a displacement of the first member 1110 relative to the second member 1120 over a distance D in radial direction, indicated by the arrow 1160, will not, or hardly, affect the magnetic flux resistance along the flux path 1140. [00085] As a result, the reluctance actuator 1100 according to the present invention provides, due to the design characteristics mentioned above, an additional operational freedom for the positioning device that moves the object in the horizontal direction.

[00086] With respect to the application of the one or more permanent magnets to generate a bias magnetic flux along a magnetic flux path of the reluctance actuator according to the invention, it can be mentioned that these can be positioned in either the first member and/or the second member, it can also be pointed out that the one or more permanent magnets may be applied at various locations in the first member and/or the second member, substantially without affecting the operation of the actuator.

[00087] With respect to the magnetic flux path and the magnetic fluxes caused by the permanent magnet and the coil of the actuator according to the invention, it can be pointed out that the magnetic flux path of the bias magnetic flux, generated by the permanent magnet, need not be the same as the magnetic flux path of the variable magnetic flux, generated by the coil. The reluctance actuator 800 according to the present invention already illustrates this; the magnetic flux path of the bias magnetic flux, 840, generated by the permanent magnet 824 is different from the magnetic flux path of the variable magnetic flux, 842, generated by the coils 826. In general, the magnetic flux path of the reluctance actuator according to the present invention can comprises a first magnetic flux path followed by the bias magnetic flux and a second magnetic flux path followed by the variable magnetic flux. These first and second magnetic flux paths may be separate paths, may partially overlap or may entirely coincide with each other.

[00088] The first members and second members of the reluctance actuators according to the invention as described above form a magnetic flux path. As such, they can e.g. be manufactured using ferromagnetic materials or the like in order to provide a path with a comparatively low magnetic flux resistance.

[00089] In an embodiment of the present invention, there is provided a positioning device for positioning an object or object table, the positioning device comprising: a linear or planar motor for positioning the object or object table over comparatively large distances, the linear or planar motor comprising: a stator; a mover configured to displace the object table relative to the stator; one or more reluctance actuators according to the present invention, whereby first members of the one or more reluctance actuators are configured to be connected to the object or object table, and whereby second members of the one or more reluctance actuators are connected to the mover.

[00090] Such a positioning device may e.g. be applied in a lithographic apparatus or an exposure apparatus e.g. to position a mask table MT or substrate table WT as indicated above. As such, in an embodiment of the present invention, there is provided a stage apparatus comprising an object table and a positioning device according to the invention. The object table of the stage apparatus can e.g. be a mask table or a substrate table.

[00091] Although specific reference may be made in this text to the use of a lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquidcrystal displays (LCDs), thin-film magnetic heads, etc.

[00092] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non-vacuum) conditions.

[00093] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention, where the context allows, is not limited to optical lithography and may be used in other applications, for example imprint lithography.

[00094] Where the context allows, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine -readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine -readable medium may include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g. carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world.

While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below. Other aspects of the invention are set-out as in the following numbered clauses. 1. A reluctance actuator configured to exert a substantially upward force on an object, that is displaceable by a mover of a positioning device in a horizontal direction, the reluctance actuator comprising: a first member configured to be connected to the object; a second member configured to be connected to the mover; the first and second member forming a magnetic flux path comprising a gap between the first member and the second member; a permanent magnet arranged in the magnetic flux path to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member; a coil configured to engage with either the first member or the second member and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member; a first surface of the first member and a first surface of the second member which face each other across the gap are configured to maintain a magnetic flux resistance of the magnetic flux path substantially constant for a displacement of the first member relative to the second member in the horizontal direction over a predetermined distance D.

2. The reluctance actuator according to clause 1, wherein the first member comprising a C-core arranged in a substantially vertical plane, the second member comprising a C-core arranged in a substantially horizontal plane.

3. The reluctance actuator according to clause 1, wherein the first member comprising a C-core arranged in a substantially vertical plane, the second member comprising a C-core arranged in the substantially vertical plane, the C-core of the second member substantially enclosing the C-core of the first member.

4. The reluctance actuator according to any of the preceding clauses, further comprising a connection member, the connection member having a bottom end connected to the first member and a top end configured to be connected to the object, whereby the top end is, during use, arranged above a top surface of the second member.

5. The reluctance actuator according to clause 4, wherein the connection member is a nonmagnetic member.

6. The reluctance actuator according to clause 1, wherein a width W1 of the first surface of the first member in the horizontal direction is smaller than a width W2 of the first surface of the second member in the horizontal direction.

7. The reluctance actuator according to clause 6, wherein the width Wl, the width W2 and the predetermined distance D fulfill:

W2 - Wl = D

8. The reluctance actuator according to clause 6, wherein the width Wl, the width W2 and the predetermined distance D fulfill: W2 - W1 > D

9. The reluctance actuator according to clause 1, wherein a width W1 of the first surface of the first member in the horizontal direction is larger than a width W2 of the first surface of the second member in the horizontal direction.

10. The reluctance actuator according to clause 9, wherein the width Wl, the width W2 and the predetermined distance D fulfill:

Wl - W2 = D

11. The reluctance actuator according to clause 9, wherein the width Wl, the width W2 and the predetermined distance D fulfill:

Wl - W2 > D

12. The reluctance actuator according to any of the preceding clauses, wherein the horizontal direction comprises a first horizontal direction and a second horizontal direction, the second horizontal direction being perpendicular to the first horizontal direction.

13. The reluctance actuator according to any of the preceding clauses, wherein the first surface of the first member and the first surface of the second member are substantially horizontal surfaces.

14. The reluctance actuator according to any of the preceding clauses, further comprising a sensor, such as a Hall sensor, arranged to measure a magnetic flux in the magnetic flux path.

15. The reluctance actuator according to clause 1, wherein the first member comprises a top plate and a bottom plate, the top plate and the bottom plate being parallel and spaced apart by a holder; the second member being arranged in between the top plate and the bottom plate and comprising: an inner magnetic cylinder; a radially magnetized permanent magnet arranged concentrically about the inner magnetic cylinder, as the permanent magnet; a cylindrical coil arranged about the inner magnetic cylinder, as the coil; an outer magnetic cylinder arranged concentrically about the radially magnetized permanent magnet; whereby top surfaces of the inner magnetic cylinder and the outer magnetic cylinder are spaced apart from a bottom surface of the top plate over a distance DI, forming a first gap of the gap; whereby bottom surfaces of the inner magnetic cylinder and the outer magnetic cylinder are spaced apart from a top surface of the bottom plate over a distance D2, forming a second gap of the gap.

16. The reluctance actuator according clause 15, wherein during use, the first gap is larger than the second gap, to cause the bias upward force.

17. The reluctance actuator according to clause 15 or 16, further comprising a sensor, such as a Hall sensor, arranged to measure a magnetic flux in the magnetic flux path.

18. The reluctance actuator according to clause 17, comprising a first set of Hall sensors arranged on the top surface of either the inner magnetic cylinder or the outer magnetic cylinder and a second set of Hall sensors arranged on the bottom surface of either the inner magnetic cylinder or the outer magnetic cylinder.

19. The reluctance actuator according to any of the preceding clauses, wherein the bias magnetic flux follows a first magnetic flux path of the magnetic flux path and wherein the variable magnetic flux follows a second magnetic flux path of the magnetic flux path.

20. A positioning device for positioning an object table, the positioning device comprising: a linear or planar motor for positioning the object table over comparatively large distances, the linear or planar motor comprising: a stator; a mover configured to displace the object table relative to the stator; wherein the positioning device further comprises one or more reluctance actuators according to any of the preceding clauses, whereby first members of the one or more reluctance actuators are configured to be connected to the object table, as the object, and whereby second members of the one or more reluctance actuators are connected to the mover.

21. A stage apparatus comprising an object table and a positioning device according to clause 20 for positioning the object table.

22. The stage apparatus according to clause 21, wherein the object table is configured to hold a patterning device or a substrate.

23. A lithographic apparatus comprising a stage apparatus according to clause 21 or 22.

24. An exposure apparatus comprising a stage apparatus according to clause 21 or 22.

Claims

1. A reluctance actuator configured to exert a substantially upward force on an object, that is displaceable by a mover of a positioning device in a horizontal direction, the reluctance actuator comprising: a first member configured to be connected to the object; a second member configured to be connected to the mover; the first and second member forming a magnetic flux path comprising a gap between the first member and the second member; a permanent magnet arranged in the magnetic flux path to generate a bias magnetic flux in the magnetic flux path, the bias magnetic flux causing a bias upward force on the first member; a coil configured to engage with either the first member or the second member and configured to, when energized, generate a variable magnetic flux in the magnetic flux path, the variable magnetic flux causing a variable force on the first member; a first surface of the first member and a first surface of the second member which face each other across the gap are configured to maintain a magnetic flux resistance of the magnetic flux path substantially constant for a displacement of the first member relative to the second member in the horizontal direction over a predetermined distance D.

2. The reluctance actuator according to claim 1, wherein the first member comprising a C-core arranged in a substantially vertical plane, the second member comprising a C-core arranged in a substantially horizontal plane.

3. The reluctance actuator according to claim 1, wherein the first member comprising a C-core arranged in a substantially vertical plane, the second member comprising a C-core arranged in the substantially vertical plane, the C-core of the second member substantially enclosing the C-core of the first member.

4. The reluctance actuator according to any of the preceding claims, further comprising a connection member, the connection member having a bottom end connected to the first member and a top end configured to be connected to the object, whereby the top end is, during use, arranged above a top surface of the second member.

5. The reluctance actuator according to claim 1, wherein a width W1 of the first surface of the first member in the horizontal direction is smaller than a width W2 of the first surface of the second member in the horizontal direction.

6. The reluctance actuator according to claim 1, wherein a width W1 of the first surface of the first member in the horizontal direction is larger than a width W2 of the first surface of the second member in the horizontal direction.

7. The reluctance actuator according to any of the preceding claims, wherein the horizontal direction comprises a first horizontal direction and a second horizontal direction, the second horizontal direction being perpendicular to the first horizontal direction.

8. The reluctance actuator according to any of the preceding claims, wherein the first surface of the first member and the first surface of the second member are substantially horizontal surfaces.

9. The reluctance actuator according to any of the preceding claims, further comprising a sensor, such as a Hall sensor, arranged to measure a magnetic flux in the magnetic flux path.

10. The reluctance actuator according to claim 1, wherein the first member comprises a top plate and a bottom plate, the top plate and the bottom plate being parallel and spaced apart by a holder; the second member being arranged in between the top plate and the bottom plate and comprising: an inner magnetic cylinder; a radially magnetized permanent magnet arranged concentrically about the inner magnetic cylinder, as the permanent magnet; a cylindrical coil arranged about the inner magnetic cylinder, as the coil; an outer magnetic cylinder arranged concentrically about the radially magnetized permanent magnet; whereby top surfaces of the inner magnetic cylinder and the outer magnetic cylinder are spaced apart from a bottom surface of the top plate over a distance DI, forming a first gap of the gap; whereby bottom surfaces of the inner magnetic cylinder and the outer magnetic cylinder are spaced apart from a top surface of the bottom plate over a distance D2, forming a second gap of the gap.

11. The reluctance actuator according to any of the preceding claims, wherein the bias magnetic flux follows a first magnetic flux path of the magnetic flux path and wherein the variable magnetic flux follows a second magnetic flux path of the magnetic flux path.

12. A positioning device for positioning an object table, the positioning device comprising: a linear or planar motor for positioning the object table over comparatively large distances, the linear or planar motor comprising: a stator; a mover configured to displace the object table relative to the stator; wherein the positioning device further comprises one or more reluctance actuators according to any of the preceding claims, whereby first members of the one or more reluctance actuators are configured to be connected to the object table, as the object, and whereby second members of the one or more reluctance actuators are connected to the mover.

13. A stage apparatus comprising an object table and a positioning device according to claim 12 for positioning the object table.

14. A lithographic apparatus comprising a stage apparatus according to claim 13.

15. An exposure apparatus comprising a stage apparatus according to claim 13.